Question

4. Let the period of revolution of a planet
at a distance R from a star be T. Prove
that if it was at a distance of 2R from
the star, its period of revolution will be
V8 T.​

Answer 1

According to Kepler's law ,

Here T denotes the time period and a denotes the distance between two objects

Here, when distance between planet and star is R then time period is T

means T² = kR³ [ here k is proportionality constant ]----(1)

Again, Let the time period is T' when distance between planet and star is 2R

T'² = k(2R)³ = k.8R³ -----(2)

Dividing equation (1) by (2)

T²/T'² = kR³/k8R³ = 1/8

T'² = 8T²

square root both sides,

Hence, time period will be √8T , when distance between planet and star will be 2R

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